Fluid density measurement

ABSTRACT

A wellbore tool for measuring the density of a fluid flowing in a wellbore by a photon attenuation technique includes a tube defining a flow path for the fluid, a photon source at one end of the tube, and a photon detector arranged to receive photons which have passed along the tube. In a preffered implementation, a source which emits coincident photon pairs, preferably  22 Na, is used. In this embodiment, the tube defining the fluid flow path has first and second relatively straight and aligned measurement portions disposed on opposite sides of the photon source, so that each measurement portion receives a respective photon of some of the coincident pairs for transmission longitudinally along it. Respective detectors at the other ends of the measurement portions receive respective ones of the photon pairs. The detected coincident photons are counted, and the density of the fluid is derived from the count rate.

This invention relates to methods and apparatus for fluid densitymeasurement, and is more particularly but not exclusively concerned withthe measurement of the density of fluids flowing in a wellbore.

In the evaluation of a hydrocarbon reservoir surrounding a wellbore, itis very useful to be able to measure the density of the fluid flowingfrom the reservoir and along the wellbore. One known technique formeasuring fluid density is a transverse photon attenuation measurement,in which the attenuation of gamma ray photons passing transverselythrough a pipe containing the fluid is measured: such a technique isdisclosed in our United Kingdom Patent Application No. 2,351,810.However, the technique disclosed in that patent application is primarilyintended for use in locations where spatial constraints are not toosevere. In deep wellbores of relatively small diameter, and in certainwellbore tools, the space available for the apparatus required for sucha measurement can be extremely limited.

For example, Schlumberger has developed a commercially successfulwellbore tool called a Modular Formation Dynamics Tester, usuallyabbreviated to MDT, which analyses formation fluids. The MDT withdrawsand analyses a flow stream of formation fluids generally as described inU.S. Pat. Nos. 3,859,851, 3,780,575, 4,860,581 and 4,936,139. It wouldbe desirable to provide the MDT with a module for measuring fluiddensity. However, the space available within an MDT is determined by itsinternal diameter, which is about 9 cm. Given the need for substantialwall thickness for the pipe in which the fluid flows and for the housingfor the photon source and detector in view of the high fluid pressurestypically encountered, the maximum internal diameter of the pipecontaining the fluid in an MDT module, and therefore the maximumdimension of the fluid path over which such a transverse photonattenuation measurement could be made, would be extremely small,typically not more than about 5 to 10 mm. This would make themeasurement relatively insensitive to the density of the fluid. Locallyincreasing the internal diameter of pipe, even if possible, is notlikely to be helpful, since it may well lead to sudden local expansionof the fluid, which can change the properties of the fluid in a waywhich affects the validity of the density measurement.

The problems caused by the lack of space in certain wellboreapplications for fluid density measuring apparatus based on photonattenuation are compounded by the fact that, in apparatus intended foruse in a wellbore, it is extremely desirable for operational and safetyreasons to use a low activity photon source of the kind exempt fromlicensing requirements. The use of such a- low activity sourcesubstantially increases the time required to make a density measurementof the required statistical precision, during which time the density ofthe fluid may change significantly.

It is therefore an object of the present invention to provide methodsand apparatus which are suitable for measuring the density of fluidflowing in a wellbore using a photon attenuation technique, and in whichthe abovementioned problems are alleviated.

According to a first aspect of the present invention, there is providedapparatus for measuring the density of a fluid, the apparatuscomprising:

means defining a flow path for the fluid;

a photon source;

photon detector means positioned to receive photons from the photonsource via the fluid in said flow path; and

means for determining the density of the fluid from a count rate of thephotons received by the detector means;

wherein said flow path includes a substantially straight measurementportion extending in the direction of flow of the fluid, the photonsource is positioned at one end of said measurement portion, and thephoton detector means is positioned at the other end of said measurementportion to receive photons which have passed along said measurementportion.

According to a second aspect of the invention, there is providedapparatus for measuring the density of a fluid, the apparatuscomprising:

means defining a flow path for the fluid;

a photon source;

photon detector means positioned to receive photons from the photonsource via the fluid in said flow path; and

means for determining the density of the fluid from a count rate of thephotons received by the detector means;

wherein the photon source comprises a source which emits coincidentphoton pairs, the flow path comprises two relatively straightmeasurement portions each disposed to receive a respective photon ofeach pair, the detector means comprises two detectors each arranged toreceive photons which have passed along a respective measurementportion, and the density determining means determines the density of thefluid from the count rate of coincident photon pairs detected by thedetectors.

Advantageously, the two measurement portions are substantially alignedwith each other and spaced apart, and the source is disposed betweentheir adjacent ends. Conveniently, the two measurement portions aresubstantially equal in length.

In a preferred implementation of the second aspect of the invention, thesource comprises a positron emitter such as ²²Na.

According to a third aspect of the invention, there is providedapparatus for measuring the density of a fluid, the apparatuscomprising:

means defining a flow path for the fluid;

a photon source;

photon detector means positioned to receive photons from the photonsource via the fluid in said flow path; and

means for determining the density of the fluid from a count rate of thephotons received by the detector means;

wherein the photon source is ²²Na.

Advantageously, the apparatus further comprises means responsive to thephoton detector means for counting the detected additional photonsemitted on the de-excitation of the ²²Ne daughter isotope resulting fromthe decay of the ²²Na source, in which case the density determiningmeans may be further arranged to determine the density of the fluid fromthe count rate of said detected additional photons.

The apparatus may further comprise means responsive to the photondetector means for measuring the count rate in the sum peak of thesource, whereby to determine the activity of the source.

According to a fourth aspect of the invention, there is provided amethod of measuring the density of a fluid, the method comprising thesteps of:

defining a flow path for the fluid;

irradiating the fluid in the flow path with photons from a photonsource;

detecting photons which have passed through the fluid in the flow path;and

determining the density of the fluid from a count rate of the detectedphotons;

wherein said flow path includes a substantially straight measurementportion extending in the direction of flow of the fluid, the photonsource is positioned at one end of said measurement portion, and thephoton detector means is positioned at the other end of said measurementportion to receive photons which have passed along said measurementportion.

According to a fifth aspect of the invention, there is provided a methodof measuring the density of a fluid, the method comprising the steps of:

defining a flow path for the fluid;

irradiating the fluid in the flow path with photons from a photonsource;

detecting photons which have passed through the fluid in the flow path;and

determining the density of the fluid from a count rate of the detectedphotons;

wherein the irradiating step comprises providing a photon source whichemits coincident photon pairs, the flow path defining step comprisesproviding said flow path with first and second relatively straightmeasurement portions each disposed to receive a respective photon ofeach pair for transmission therealong, and the density determining stepcomprises determining the density of the fluid from the count rate ofcoincident photon pairs detected.

The density determining step may also comprise, for an upper part of theexpected range of densities to be measured, determining the density ofthe fluid from the count rate of the photons passing along only one ofsaid measurement portions.

The photon source used in the method is preferably ²²Na, in which casethe method preferably further comprises the step of counting thedetected additional photons emitted on the de-excitation of the ²²Nedaughter isotope resulting from the decay of the ²²Na source, and mayfurther include determining the density of the fluid from the count rateof the detected additional photons.

The method may additionally include measuring the count rate in the sumpeak of the source, whereby to determine the activity of the source.

The invention will now be described, by way of example only, withreference to the accompanying drawings, of which:

FIG. 1 is a simplified schematic representation of a wellbore tool formeasuring the density of a fluid flowing in the wellbore by photonattenuation, in accordance with a first aspect of the present invention;

FIG. 2 is a simplified schematic representation of a wellbore tool formeasuring the density of a fluid flowing in the wellbore by photonattenuation, using a photon source which emits coincident photon pairs,in accordance with a second and preferred aspect of the presentinvention;

FIG. 2A shows a preferred embodiment of a principal part of the tool ofFIG. 1;

FIG. 3 shows the decay scheme for a preferred photon source used in thetool of FIG. 2;

FIG. 4 is a graph of showing the how photon count rates vary withdensity for single and coincident photon detection in the tool of FIG.2; and

FIG. 5 is a graph of relative density sensitivity for single andcoincident photon detection in the tool of FIG. 2.

The wellbore tool illustrated in FIG. 1 is indicated generally at 10,and principally comprises a flow-line 12 shaped to define asubstantially straight measurement portion 14 connected betweenlaterally offset inlet and outlet portions 16, 18 which aresubstantially aligned and extend generally parallel to the measurementportion. As already mentioned, FIG. 1 is a simplified schematicrepresentation of the tool 10, which in practice is mounted within ahousing adapted to form a module for inclusion in an MDT. The MDT is inturn adapted to be lowered to a desired depth in the wellbore, e.g. onthe end of a wireline or coiled tubing, and to extract formation fluidsfrom the formations surrounding the borehole as described in theaforementioned United States patents.

Positioned at one end of the measurement portion 14 of the flow-line 12is a low activity gamma ray photon source 20, for example alicence-exempt ¹³³Ba source, while positioned at the other end of themeasurement portion 14 is a photon detector 22, such as a combined NaIscintillator crystal and photomultiplier. The source 20 emits gamma rayphotons, some of which pass longitudinally along the measurement portion14 of the flow-line 12, through the fluid flowing in the measurementportion. A cylindrical collimator 24 made of a heavy metal such as leador tungsten coaxially surrounds the measurement portion 14. The photonswhich have passed along the measurement portion 14 of the flow-line 12are detected by the detector 22, and their count rate is measured aswill become apparent hereinafter.

Since the attenuation of the photons passing along the measurementportion 14 of the flow-line 12 is dependent on the density of the fluidflowing along the measurement portion, the count rate of the photonsdetected by the detector 22 is also dependent on the density of thefluid. The relationship between the count rate, n, with fluid present,can be expressed as$\frac{n}{n_{0}} = {\exp\left( {{- \mu}\quad\rho\quad x} \right)}$where n₀ is the count rate with no fluid present, μ is an attenuationcoefficient which depends on the photon energy spectrum, ρ is the fluiddensity and x is the attenuation path length, ie the length of themeasurement portion 14.

Because the photons pass longitudinally along the flow-path 14, theattenuation path length can be made much greater than would be possiblefor the abovementioned prior art transverse photon attenuationmeasurement, typically up to about 30 cm. As a result, the densitysensitivity of the tool 10 is considerably improved in relation to thedensity sensitivity which could be achieved with a transverse photonattenuation measurement effected under the same dimensional constraints.

Although the longitudinal photon attenuation measurement effected by thetool 10 is a substantial improvement over that obtainable if atransverse photon attenuation measurement were to be used in the tool,the longitudinal measurement nevertheless suffers from the disadvantagethat the aperture of the measurement is very small. The preferredimplementation of the invention illustrated in FIG. 2 is intended toalleviate this drawback.

Thus the wellbore tool of FIG. 2 is indicated generally at 50, andprincipally comprises a flow-line 52 shaped to define two substantiallystraight measurement portions 54, which are spaced apart, substantiallyaxially aligned with each other, and connected in series with each otherby a U-shaped connecting portion 55. The flow assembly comprising themeasurement portions 54 and the connecting portion 55 is connectedbetween laterally offset inlet and outlet portions 56, 58, which aresubstantially aligned and extend generally parallel to the measurementportions. As mentioned earlier, FIG. 2 is a simplified schematicrepresentation of the tool 50, which, like the tool 10 of FIG. 1, isagain in practice is mounted within a housing adapted to form a modulefor inclusion in an MDT. The MDT is in turn adapted to be lowered to adesired depth in the wellbore, eg on the end of a wireline or coiledtubing, and to extract formation fluids from the formations surroundingthe borehole as described in the aforementioned United States patents.

Positioned between the adjacent ends of the measurement portions 54 ofthe flow-line 52, in the space defined by the limbs of the U-shapedconnecting portion 55, is a low activity, licence-exempt, gamma rayphoton source 60. But in the tool 50, the source 60 is a source whichemits coincident photon pairs, preferably a positron emitter such as²²Na, although the use of other suitable multi-line gamma ray sources isalso possible. Respective tubular collimators 61, each similar to thecollimator 24 of FIG. 1, coaxially surround the measurement portions 54.

In the case of positron emitters, the decay particle annihilates with anelectron in surrounding matter, with the particle rest masses (511keV/c² for each of the annihilating e⁺e⁻ pair) converted to energy inthe form of electromagnetic radiation. The typical momenta of theemitted positron and the annihilation electron are small compared to themomentum of photons of the released mass energy, and therefore a pair ofback-to-back photons, each of energy 511 keV, is created to conserveboth momentum and energy. In the case of ²²Na, a gamma ray of energy1275 keV is also emitted in the de-excitation of the ²²Ne daughterisotope. The decay scheme for ²²Na is shown in FIG. 3.

The tool 50 further includes two similar photon detectors 62, similar tothe detector 22 of the tool 10 of FIG. 1. The detectors 62 are disposedat the respective other ends of the measurement portions 54 of theflow-path 52, so that each photon of an annihilation pair must passlongitudinally along a respective measurement portion, through thefluid, before reaching the respective detector. The detectors 62 arediametrically opposed with respect to the photon source 60. Ideally, thedistance to each detector is the same, although other arrangements mayhave advantages in certain circumstances, as will hereinafter beexplained.

FIG. 2A shows a practical implementation of the main flow line 52 andassociated components of the tool 50, like components being designatedby the same reference numbers as were used in FIG. 2. Thus the flow line52 and the measurement portions 54 are formed as a single straight tube80 with titanium end caps 82, with the inlet and outlet portions 56, 58extending radially of the tube at each end of the tube. The collimators61 are formed in one piece, indicated at 61 a, which has extensions 84at each end. The extensions 84 extend a little beyond the titanium endcaps 82 on the tube 80, and have an increased internal diameter (inrelation to the main part of the collimator 61), while the detectors 62are positioned at the extremities of respective ones of the extensions84, facing respective ones of the titanium end caps.

The source 60 is double-encapsulated to withstand 25 kPSI, and ismounted in a tubular source holder 86 which is mounted so as to extenddiametrically across the tube 80 midway along the length of the tube,with the source 60 positioned substantially on the axis of the tube. Thetubular source holder 86 has oppositely disposed cutaway windows 88facing in opposite directions along the axis of the tube 80, towards thedetectors 62

The respective outputs of the detectors 62 of the tool 50 are analysedin terms of energy and timing by signal processing circuitry 64. Thecircuitry 64 comprises two similar signal processing chains, eachcomprising an amplifier 65, a single channel analyzer 66 which selectsonly those outputs from the respective detector corresponding to photonswithin a certain energy range, and an adjustable delay circuit 68, allconnected in series. A respective one of these signal processing chainsis connected between a respective detector 62 and a respective input ofa coincidence circuit 70, which produces an output only in response tocoincident photons in the selected energy range. The output of thecoincidence circuit is applied to a counter/scaler and dataacquisition/transmission unit 72.

For a ²²Na source of activity S Bq (decays/s), 2S photons per second ofenergy 511 keV each are produced. The single 511 keV photon count ratein each detector 62 of a symmetrical, identical pair of detectors canthen be written asn ₁=2S(σ/4n)ε₁ε_(w) exp(−μρx)where σ is the solid angle subtended by each detector, ε₁ is thedetection efficiency of the detector, ε_(w) describes the transmissionthrough the wall of the source container and the walls of the flow-line52, and each photon beam passes through an attenuation path length x.Losses in the wall of the source container and in the flow-line wallscan be kept to a very low level. Loss of photon flux in the fluid,represented by the exponential term, is of course desirable, since itprovides the measurement signal. As already mentioned, the coincidencecircuit 70 produces an output for each coincident photon event detectedin both detectors: a coincidence count rate can be derived as follows.The source activity and solid angle do not feature again, since eachphoton reaching the first detector 62 is accompanied by a partneremitted at 180°, i.e. towards the second detector 62. The coincidencerate is lower than n₁ in proportion to the efficiency of the seconddetector 62 (ε₂) and the transmission efficiency through the flow-linewalls of the second photon. Crucially, however, the coincidence rate isalso reduced by a factor of e^(−μρx) due to attenuation in fluid in thesecond measurement portion 54 of the flow-line 52.Thus the count rate for coincident two-photon events can be written as:n _(coin)=2S(ρ/4n)ε₁ε₂ε_(w)ε_(w) exp(−μρx)exp(−μρx)orn _(coin)=2S(σ/4n)ε₁ε₂ε_(w)ε_(w) exp(−μρ2x)

It can thus be seen that the coincidence rate has density contrastequivalent to a path length of 2x, while achieving solid angleefficiency σ corresponding to an attenuation length of only x. Thisgives an increase in count rate efficiency of a factor of 4 compared toa single photon measurement with the same density sensitivity, althoughsmall losses will be introduced due to the efficiency of the seconddetector and losses in transmission of the second photon through theflow-line walls. These losses can be made to be relatively small. Withan electronic coincidence requirement, a very wide spectroscopy windowcan be applied to each detector, requiring only the suppression of lowenergy noise and the high-energy 1275 keV photon. With thin walls ofstrong, low-density materials, the transmission through the flow-linewalls may be close to 100%.

Importantly, the innovative features of the tool 50 permit an extremelycompact geometry to be achieved, with detectors subtending a relativelylarge solid angle, while maintaining a relatively long effectiveattenuation path length.

However, many modifications can be made to the tool 50, in order thatcertain other advantages are also achieved.

Thus, FIG. 4 shows the relative count rates for singles events (511 keVphotons registering in either detector 62) and coincidence events (a 511keV photon registering in both detectors 62 within a short time window)normalised to the count rate for an empty sample volume (n₀). Because ofthe exponential nature of the response function, the sensitivity of thecoincidence measurement decreases with increasing attenuation. So theprecision of measurements for densities in the range 0.5-1.0 g/cc islower than for densities below 0.5 g/cc. Optimal ranges can be selectedby a choice of appropriate path length in each sample volume. Theresponse can be increased at high densities by choosing a shorterattenuation path, which is possible by measuring also singles events(with photons passing through only one arm of the sample fluid), wherethe requirement is only that at least one detector of the pair registersan event. FIG. 5 shows the measurement sensitivity, ie the negativegradient of the count rate curves of FIG. 4, as a function of density.The graph shows clearly that, for a suitably chosen geometry, acoincidence measurement has twice the sensitivity of a singlesmeasurement at low densities, while at higher densities (˜0.8-1.0 g/cc)the reverse is the case. In practice, an intelligent interpretationalgorithm is used to choose the more appropriate interpretation mode.

The dynamic range of the measurement can be further extended by usingsingle 1275 keV events to measure very high densities, since thesephotons exhibit a lower attenuation coefficient. By an appropriatechoice of sample volume length, the tool can be optimised for thehighest precision from coincident 511 keV events at low densities,singles 511 keV events at intermediate energies, and single 1275 keVevents at the highest energies. In this implementation of the invention,at least one of the single channel analysers 66 of FIG. 2 is replaced bya multichannel analyser producing outputs for both 511 keV events and1275 keV events.

Additionally, it is possible to make a determination of the ²²Na sourceactivity by measuring the count rate in the so-called “sum peak”, wherea 1275 keV photon deposits its full energy in the detector crystalsimultaneously with one of the 511 keV photons, giving an event of sumenergy 1786 keV. The count rates for the 511 keV peak, the 1275 keV peakand the sum peak can be written as follows:n ₅₁₁=2S(σ/4n)ε₅₁₁n ₁₂₇₅ =S(σ/4n)ε₁₂₇₅n _(sum)=2S(σ/4n)ε₅₁₁(σ/4n)ε₁₂₇₅Combining these gives $\begin{matrix}{\frac{n_{511} \cdot n_{1275}}{n_{sum}} = \frac{2{S^{2}\left( {{\sigma/4}\quad\pi} \right)}^{2}\quad ɛ_{511}ɛ_{1275}}{2{S\left( {{\sigma/4}\quad\pi} \right)}^{2}\quad ɛ_{511}ɛ_{1275}}} \\{S = \frac{n_{511} \cdot n_{1275}}{n_{sum}}}\end{matrix}$

Thus it is possible to maintain an online source activity calibration,and to implement an alarm to replace the source when its activity hasdropped significantly. The half-life of ²²Na is 2.6 years.

Many other modifications can be made to the described embodiments of theinvention.

For example, multi-line gamma ray photon sources other than ²²Na or¹³³Ba can be used, eg ⁶⁰Co. In the case of ¹³³Ba and ⁶⁰Co sources, thephotons are not emitted back-to-back, so that it is not strictlynecessary for the source and detectors to be aligned in a straight line,as in the tool 50. However, since this arrangement is advantageous forcompactness reasons, it is likely to be preferred.

And although the described embodiments of the invention uselicence-exempt gamma ray sources, the use of an X-ray source, in theform of a downhole X-ray generator, is also possible. While such asource is more complex and expensive, and has certain otherdisadvantages in relation to the preferred gamma ray source, it also hascertain advantages, particularly with regard to sensitivity to fluiddensity and the statistical precision of the measurement.

1. Apparatus for measuring the density of a fluid, the apparatuscomprising: means defining a flow path for the fluid; a photon source;photon detector means positioned to receive photons from the photonsource via the fluid in said flow path; and means determining thedensity of the fluid from a count rate of the photons received by thedetector means; wherein said flow path includes a substantially straightmeasurement portion extending in the direction of flow of the fluid, thephoton source is positioned at one end of said measurement portion, andthe photon detector means is positioned at the other end of saidmeasurement portion to receive photons which have passed along saidmeasurement portion.
 2. Apparatus for measuring the density of a fluid,the apparatus comprising: means defining a flow path for the fluid; aphoton source; photon detector means positioned to receive photons fromthe photon source via the fluid in said flow path; and means fordetermining the density of the fluid from a count rate of the photonsreceived by the detector means; wherein the photon source comprises asource which emits coincident photon pairs, the flow path comprises tworelatively straight measurement portions each disposed to receive arespective photon of each pair, the detector means comprises twodetectors each arranged to receive photons which have passed along arespective measurement portion, and the density determining meansdetermines the density of the fluid from the count rate of coincidentphoton pairs detected by the detectors.
 3. Apparatus as claimed in claim2, wherein the two measurement portions are substantially aligned witheach other and spaced apart, and the source is disposed between theiradjacent ends.
 4. Apparatus as claimed in claim 2, wherein the two flowpath portions are substantially equal in length.
 5. Apparatus as claimedin claim 2, wherein the source comprises a positron emitter. 6.Apparatus as claimed in claim 5, wherein the photon source is ²²Na. 7.Apparatus for measuring the density of a fluid, the apparatuscomprising: means defining a flow path for the fluid; a photon source;photon detector means positioned to receive photons from the photonsource via the fluid in said flow path; and means for determining thedensity of the fluid from a count rate of the photons received by thedetector means; wherein the photon source is ²²Na.
 8. Apparatus asclaimed in claim 6, further comprising means responsive to the photondetector means for counting the detected additional photons emitted onthe de-excitation of the ²²Ne daughter isotope resulting from the decayof the ²²Na source.
 9. Apparatus as claimed in claim 8, wherein thedensity determining means is further arranged to determine the densityof the fluid from the count rate of said detected additional photons.10. Apparatus as claimed in claim 6, further comprising means responsiveto the photon detector means measuring the count rate in the sum peak ofthe source, whereby to determine the activity of the source.
 11. Amethod of measuring the density of a fluid, the method comprising thesteps of: defining a flow path for the fluid; irradiating the fluid inthe flow path with photons from a photon source; detecting photons whichhave passed through the fluid in the flow path; and determining thedensity of the fluid from a count rate of the detected photons; whereinsaid flow path includes a substantially straight measurement portionextending in the direction of flow of the fluid, the photon source ispositioned at one end of said measurement portion, and the photondetector means is positioned at the other end of said measurementportion to receive photons which have passed along said measurementportion.
 12. A method of measuring the density of a fluid, the methodcomprising the steps of: defining a flow path for the fluid; irradiatingthe fluid in the flow path with photons from a photon source; detectingphotons which have passed through the fluid in the flow path; anddetermining the density of the fluid from a count rate of the detectedphotons; wherein the irradiating step comprises providing a photonsource which emits coincident photon pairs, the flow path defining stepcomprises providing said flow path with first and second relativelystraight measurement portions each disposed to receive a respectivephoton of each pair for transmission therealong, and the densitydetermining step comprises determining the density of the fluid from thecount rate of coincident photon pairs detected.
 13. A method as claimedin claim 12, wherein the density determining step comprises, for anupper part of the expected range of densities to be measured,determining the density of the fluid from the count rate of the photonspassing along only one of said measurement portions.
 14. A method asclaimed in claim 12, wherein the photon source is ²²Na, and furthercomprising the step of counting the detected additional photons emittedon the de-excitation of the ²²Ne daughter isotope resulting from thedecay of the ²²Na source.
 15. A method as claimed in claim 14, furthercomprising determining the density of the fluid from the count rate ofthe detected additional photons.
 16. A method as claimed in claim 12,further comprising measuring the count rate in the sum peak of thesource, whereby to determine the activity of the source.